The present invention concerns, in general terms, a method and a device for the processing of data, notably the representation, generation, retrieval, regeneration or iterative processing of data.
More particularly, the present invention relates to the transmission (that is to say the remote representation) and/or the storage (that is to say the representation in a memory) of data, with or without compression thereof. These data can advantageously consist of the digital or analogue data of an image or sequence of images, and/or the digital or analogue data relating to sound (music, speech, etc) and/or the digital or analogue data relating to any mono or multi-dimensional signal. More generally, the present invention relates to the representation of any mono or multi-dimensional data.
Before disclosing the objectives and means of the invention, it is proposed to give below the following definitions:
xe2x80x9cSet of dataxe2x80x9d: set of any data representing physical quantities (usually voltage levels) which can themselves represent other physically perceptible or measurable quantities. In favoured mappings, the sets of data concerned are images, sound or mono or multi-dimensional signals, etc. In the mapping concerning the processing of images, reference will sometimes be made to the xe2x80x9cimagexe2x80x9d instead of the xe2x80x9cset of dataxe2x80x9d relating to the image. That which will be disclosed below with regard to xe2x80x9cimagesxe2x80x9d or xe2x80x9csub-imagesxe2x80x9d is respectively applicable to xe2x80x9csets of dataxe2x80x9d or xe2x80x9csub-sets of dataxe2x80x9d and vice versa.
xe2x80x9cRepresentation of dataxe2x80x9d: any xe2x80x9cprocessingxe2x80x9d of a set of data of a given type, resulting a perfect or imperfect transformation of the said set of data into another type. Example: the data can consist of the 256 grey levels of the pixels of an image, their representation consisting of a series of binary words able to be stored or transmitted; conversely, the representation of the data consisting of the said binary words can consist of their transformation in order once again to have data of the same type as the initial data.
xe2x80x9cPrimary representationxe2x80x9d: by convention, any processing resulting in the transformation of data of a first type into data of a second type. In this case the term xe2x80x9cprimary processingxe2x80x9d of the data will be used.
xe2x80x9cSecondary representationxe2x80x9d: by convention, the transformation of data of the second type resulting from a primary processing. In this case the term xe2x80x9csecondary processingxe2x80x9d will be used.
xe2x80x9cRetrieval of dataxe2x80x9d: the particular case of a secondary representation in which the data of the second type are transformed into data of the first type. This retrieval can be perfect or imperfect.
A xe2x80x9cmetric spacexe2x80x9d is a set of elements provided with a functional distance which is symmetrical and positive and satisfies the triangular inequality. This space is xe2x80x9ccompletexe2x80x9d when it contains all the limit points of all the convergent sequences.
A xe2x80x9cLipschitz mappingxe2x80x9d: a mapping which transforms the points of a is metric space in the same space and for which all the ratios of the distance of two elements transformed by the said mapping to the distance of the said two elements are bounded.
A xe2x80x9ccontractive mappingxe2x80x9d or xe2x80x9ccontractionxe2x80x9d: a Lipschitz mapping for which the smallest of the majorants (contraction factor) of the said set of ratios is less than unity. However, within the meaning of the present invention, all convergent mappings (successive approximations) in a sub-set of the metric space are contractive.
A xe2x80x9csimilarityxe2x80x9d is a Lipschitz mapping for which the ratio of the distance of two transformed elements to the distance of the said elements is a fixed quantity. A linear similarity is a xe2x80x9csimilitudexe2x80x9d.
A xe2x80x9ccontractive similarityxe2x80x9d is a Lipschitz mapping for which the ratio of the distance of two transformed elements to the distance of the said elements is a fixed quantity strictly less than unity.
The xe2x80x9cfixed pointxe2x80x9d of a contraction of a complete metric space in the same space (or of a sub-set of this space in itself) is the single element of the space which is left invariant by the said contractive mapping.
The xe2x80x9cconstructionxe2x80x9d of a contractive mapping on a set of data consists of constituting a family of contractions able to transform the data and select the parameters of one of the said contractions in order to satisfy one or more predetermined conditions.
The xe2x80x9cmethod of successive approximationsxe2x80x9d makes it possible to iteratively approach the fixed point of a contraction as close as is desired. Starting from an arbitrary element, the said contraction is applied to this arbitrary element. The same contraction is then applied to the previously obtained transform. By reiterating this process the single fixed point of the contraction is successively and ineluctably approached.
xe2x80x9cA best approximationxe2x80x9d of an element in a metric space is a point of a sub-set of candidates, which are themselves points of the said space, which minimises the distance to the said element.
xe2x80x9cA good approximationxe2x80x9d of an element in a metric space is a point of a sub-set of the said space which is close with a predetermined error, to a predetermined best approximation.
In the prior art, various image representation methods, with compression, are known, using the so-called xe2x80x9cfractalxe2x80x9d technique.
Through the document U.S. Pat. No. 5,065,447, a method and a device are known for processing or storing an image with compression of the data relating to the initial image. In this method, the data relating to the initial image are divided, that is to say the image is cut into a plurality of elementary sub-images (referred to as xe2x80x9cdomain blocksxe2x80x9d). This method then consists of generating an ordered dictionary of a set of reference sub-images (referred to as xe2x80x9crange blocksxe2x80x9d) formed from image portions of predetermined size which have undergone a certain number of predetermined operations such as rotation and turning on various axes of symmetry. Then, for each elementary sub-image, a comparison is carried out with all the reference sub-images of the dictionary and in the dictionary the reference sub-image is selected which is the most similar to the elementary sub-image in question. Finally, the method consists of processing or storing parameter information relating to the addresses of the reference sub-images selected in the dictionary, in order to represent each of the original elementary sub-images.
It is through this set of operations that the method described in this document makes it possible to obtain a first representation of the image with compression of the data.
In order to effect, using the said parameter information, the retrieval of the initial image, the method and device described in this document perform the following operations: using an arbitrary starting image, steps similar to those above are carried out, that is to say the arbitrary starting image is partitioned and a dictionary is formed from the elementary sub-images thereof. However, the dictionary is formed only partially, performing for each sub-image only the predetermined operation corresponding to the relevant address of the dictionary of the sub-image in question.
The data thus obtained are used in order to reiterate this process until the difference between two consecutively obtained images is less than a predetermined threshold. The image lastly obtained is then an approximation of the initial image.
This method, which is interesting on a theoretical level, has the major drawback that it is sometimes difficult to put into practice on an industrial level with the means known at the present time. This is because each image must give rise to a long analysis with the formation of a particularly large dictionary, the elementary sub-images of the image to be stored or to be transmitted all being compared with each of the reference sub-images present in the dictionary. The inventors, who carried out simulations, found that, for certain images of average size and resolution (512xc3x97512 pixels with 3xc3x97256 colour levels), the processing time for the compression was of the order of 1000 to 2000 seconds on a workstation, that is to say around half an hour. Such a processing time is obviously prohibitive for almost any industrial application.
Through the document WO-A-93/17519, another method and device are known for processing images with compression of the data relating to the initial image. In this method the data relating to the initial image are also partitioned, that is to say the image is divided into a plurality of elementary images (referred to as xe2x80x9cdomainsxe2x80x9d). In this method a set of fractal transforms connecting the sub-images to all the initial data is then determined, that is to say, in the initial image, an image portion similar to the elementary image in question is sought, so as to minimise any error between the initial data and the approximate data item thus obtained. The coefficients of all the fractal transformations thus performed constitute the first representation of the initial image.
In order to perform the retrieval of the image, the method and device described in this document seek out the fixed points of the elementary fractal transformations whose coefficients were received without however explaining how this search is effected. The initial image is thus retrieved by carrying out a combining of the retrieved sub-images.
This method is also interesting on a theoretical level. However, the inventors found significant degradations in the quality of the image retrieved.
The inventors sought to develop a data processing method of the same type as the methods of the prior art analysed above, but having better performance both with regard to the quality of the retrieved data and with regard to the processing speed.
In the course of their researches, the inventors discovered that the reason why the methods described in U.S. Pat. No. 5,065,447 and WO-A-93/17519 have the above-mentioned defects relates to the fact that the two methods use geometric transformations of image portions consisting essentially of contractive similarities (construction of the dictionary in U.S. Pat. No. 5,065,447 and fractal transformation in WO-A-93/17519). They were in fact able to show that it is a question in both cases of implementing an idea widely shared by experts interested in fractal compression at the time of filing of the present application, an idea according to which the images would, whatever their origin, consist essentially of elements or parts having significant degrees of resemblance between them.
In fact, however, the performance of WO-A-93/17519 is very poor with regard to the quality of the retrieved image since the inventors discovered that the capabilities of retrieval of contractive similitudes are very limited, contrary to the belief of experts at the date of filing of the present application.
Likewise the performance of U.S. Pat. No. 5,065,447 is very limited with regard to processing time. As the retrieval capabilities of contractive similitudes are inclusively limited, the author of U.S. Pat. No. 5,065,447 was led to the production of a large dictionary constructed on the basis of numerous transformations of sub-images in the method according to U.S. Pat. No. 5,065,447: it is a case in fact of artificially multiplying the resemblance elements, which certainly makes it possible to improve the quality of the retrieved image substantially, but at the expense of the computing time.
The inventors therefore sought to produce a method and a device for processing data, notably for images, making it possible to obtain better performance than the aforesaid prior art, both with regard to the quality of the data or of the retrieved image and with regard to the computing speed, and able to result in a significant compression of the data to be transmitted or stored.
The methods and devices according to the invention resolve this problem.
In general terms, the present invention relates first of all to a method for the primary processing of a set of data representing physical qualities, characterised in that it includes:
b) a step of xe2x80x9cconstructionxe2x80x9d of a global contractive mapping of the so-called xe2x80x9cfirst typexe2x80x9d for the said set of data, the fixed point of which constitutes an approximation of all or part of this set, using, to do this, at least one mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings and determining the parameters of the global contractive mapping so as:
to allow the use of a method of successive approximations converging towards the fixed point of the said global contractive mapping; the set of parameters thus determined constituting a primary representation of the said set of data.
In general terms, the present invention then relates to a device for the primary processing of a set of data representing physical quantities, characterised in that it includes:
means of inputting data to be processed;
means of outputting parameters;
first logic means of transforming the data to be processed into parameters;
the said first logic means including:
xe2x80x9cconstructionxe2x80x9d means adapted:
to construct, for each set of data to be processed, a global contractive mapping of the so-called xe2x80x9cfirst typexe2x80x9d, the fixed point of which constitutes an approximation of all or part of this set of data, using, to do this, at least one mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings, so as:
to allow the use of a method of successive approximations converging towards the fixed point of the said global contractive mapping;
to deliver, at the output means, the parameters thus determined, said parameters constituting a primary representation of the said set of data.
By virtue of these provisions, the present invention achieves these objectives.
It should be noted first of all that it was discovered that, in general terms, in accordance with the invention, in order to process, notably to represent, a set of initial data representing physical quantities, notably with compression of the said initial data, it suffices to construct, by appropriate means, a global contractive mapping, acting on the said data.
Another important characteristic of the invention lies in the fact that, in order to construct the said global contractive mapping, it is necessary to use, to do this, at least one mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings. In doing this, any recourse to mathematical transformations belonging to the class of contractive similarities is excluded, which makes it possible to avoid the drawbacks set out above.
However, in order to construct the said global contractive mapping acting on the data, the expert has at his disposal a very wide range of mathematical tools on which he is able to draw. He can consequently choose from amongst these tools those which are the most favourable to performance, for example in conjunction with the type of data to be represented or the particular application involved. Such a possibility does not exist in the prior art analysed above and proves highly advantageous. Thus, for example, in the case of a local processing of the image, by partitioning of said image into elementary sub-images, the expert can choose, for the local processing, mappings which are not necessarily contractive, which gives him an important choice in the possibilities of local processing of the image and also leaves him a great deal of freedom. In particular, he can choose, at local level, Lipschitz mappings which enable him to facilitate the implementation of the contractive nature of the global mapping.
Moreover, the use of a method of successive approximations leaves the expert the freedom to choose the final difference between the said fixed point and the data thus retrieved or generated.
In one of its aspects, the present invention relates in particular to a method of primary processing of a set of data representing physical quantities comprising:
a) a xe2x80x9cpartitioningxe2x80x9d step in the course of which the said set of data is partitioned into m xe2x80x9celementary sub-setsxe2x80x9d;
characterised in that it also includes:
b) a xe2x80x9cconstructionxe2x80x9d step in which, for each of the said elementary sub-sets, n working sub-sets are taken into consideration, n being greater than 1, and an elementary mapping of the n working sub-sets is constructed in the elementary sub-set in question, determining the parameters of the elementary mapping so as:
to make contractive a global mapping, of the so-called xe2x80x9cfirst typexe2x80x9d,including the m elementary mappings related to the m elementary sub-sets and the fixed point of which constitutes an approximation of all or part of this set of data;
to allow the use of a method of successive approximations converging towards the fixed point of the global contractive mapping;
all the said parameters thus determined and related to the m elementary sub-sets constituting a primary representation of the said set of data.
Moreover, in this aspect, the present invention relates to a device for the primary processing of a set of data representing physical quantities, characterised in that it includes:
means of inputting data to be processed;
means of outputting parameters;
first logic means for transforming the data to be processed into parameters; the said first logic means including:
xe2x80x9cpartitioningxe2x80x9d means adapted to partition the said set of data into m xe2x80x9celementary sub-setsxe2x80x9d;
xe2x80x9cconstructionxe2x80x9d means adapted:
to take into account, for each of the said elementary sub-sets, n working sub-sets, n being greater than 1,
to construct, for each of the elementary sub-sets, an elementary mapping of the n working sub-sets in the elementary sub-set in question, determining the parameters thereof so as:
to make contractive a global mapping of the so-called xe2x80x9cfirst typexe2x80x9d including the m elementary applications related to the m elementary sub-sets, and the fixed point of which constitutes an approximation of all or part of this set of data, and
to permit the implementation of a method of successive approximations converging towards the fixed point of the said global contractive mapping;
to deliver at the output means the parameters thus determined, said parameters constituting a primary representation of the said set of data.
By virtue of these provisions, the method and device overcome the aforementioned drawbacks.
In fact, it should be noted first of all that the method and device allow a representation of a set of data, notably those relating to an image, with where applicable a significant amount of compression.
In addition, considering n working sub-sets (or working sub-images), n being strictly greater than unity, according to the invention a multi-dimensional mapping is used, which excludes the mapping belonging to the class of similarities. Because of this, the method according to the invention avoids the poor performance related to the use of fractal transforms as described in the document WO-A-93/17519. This is because, by constructing each elementary mapping in question from the n working sub-sets, the quality of the retrieval is notably improved, in so far as the number n of working sub-sets is high. Certainly the computing time increases with the number of working sub-sets used by the elementary sub-sets (or elementary sub-images) but this computing time, even for a relatively high integer n, is much less than the computing time related to the construction of a dictionary and the analysis of the image on this basis described in the document U.S. Pat. No. 5,065,447.
Thus, by choosing, in a preferred embodiment, n equal to 4, the inventors found, with regard to quality, that the method according to the invention made possible, all other things being equal, an improvement in the error rate of approximately 15% compared with the method and device described in the document WO-A-93/17519.
Moreover, by avoiding the formation of a dictionary and the long analysis described in the document U.S. Pat. No. 5,065,447, and by virtue of the characteristics of the present invention, the processing of an image is notably accelerated compared with the aforementioned US document. By implementing their preferred embodiment, the inventors found that, for an image of 512xc3x97512 pixels with 3xc3x97256 colour levels, the processing time was of the order of less than 100 seconds on a workstation; they also have every reason to believe that the improvements made to the method and device briefly described above will make it possible to obtain performance with regard to speed.
As a variant, in a second aspect of the present invention, the method of primary processing of a set of data representing physical quantities comprises:
a) a xe2x80x9cpartitioningxe2x80x9d step in the course of which the said set of data is partitioned into m xe2x80x9celementary sub-setsxe2x80x9d; and it is characterised in that it also includes:
b) a xe2x80x9cconstructionxe2x80x9d step in which, for each of the said elementary sub-sets, n working sub-sets are taken into consideration, related geometrically thereto in a predetermined manner, n being non null, and an elementary mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings is constructed, from the n working sub-sets in the elementary sub-set in question, determining all the parameters of this elementary mapping so as:
to make contractive a global mapping, of the so-called xe2x80x9cfirst typexe2x80x9d, including the m elementary mappings related to the m elementary sub-sets and the fixed point of which constitutes an approximation of all or part of this set of data;
to allow the use of a method of successive approximations converging towards the fixed point of the said global contractive mapping;
all the said parameters thus determined and related to the m elementary sub-sets constituting a primary representation of the said set of data.
In this aspect of the present invention, the device for the primary processing of a set of data representing physical quantities includes:
means of inputting data to be processed;
means of outputting parameters;
first logic means of transforming the data to be processed into parameters; the said first logic means including:
xe2x80x9cpartitioning means adapted to partition the said set of data into xe2x80x9celementary sub-setsxe2x80x9d,
xe2x80x9cconstructionxe2x80x9d means adapted:
to take into account, for each of the said elementary sub-sets, n working sub-sets related thereto in a predetermined fashion, n being non-null,
to construct, for each of the elementary sub-sets, an elementary mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings, of the n working sub-sets in the elementary sub-set in question, determining all the parameters of this elementary mapping so as:
to make contractive a global mapping of the so-called xe2x80x9cfirst typexe2x80x9d including the m elementary mappings whose fixed point constitutes an approximation of all or part of this set of data;
to allow the use of a method of successive approximations converging towards the fixed point of the said global contractive mapping;
to deliver, at the output means, the parameters thus determined, said parameters constituting a primary representation of the said set of data.
These arrangements have substantially the same advantages as those relating to the first aspect of the present invention as described briefly above.
It will also be noted here that, like the constructed elementary mappings belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings, the mappings belonging to the class of similitudes is avoided, with the advantages observed above.
In addition, as the n working sub-sets relating to a given elementary sub-set are related geometrically in a predetermined manner thereto, this aspect of the invention advantageously makes it possible to avoid the long analysis with the formation of a dictionary followed by a search for the reference sub-image as described in the document U.S. Pat. No. 5,065,447. The speed of processing of a set of data, and notably of an image, is thereby considerably increased.
As a variant, in a second aspect of the present invention, the method of primary processing of a set of data representing physical quantities comprises:
a) a xe2x80x9cpartitioningxe2x80x9d step in the course of which the said set of data is partitioned into m elementary sub-setsxe2x80x9d; and also includes:
b) a xe2x80x9cconstructionxe2x80x9d step in which, for each of the said elementary sub-sets, n working sub-sets which correspond to it are taken into consideration, at least one working sub-set having a size different from that of the corresponding elementary sub-set, n being non null, and an elementary mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings is constructed, of the n working sub-sets in the elementary sub-set in question, determining all the parameters of this elementary mapping so as:
to make contractive a global mapping, of the so-called xe2x80x9cfirst typexe2x80x9d, including the m elementary mappings related to the m elementary sub-sets, the fixed point of which constitutes an approximation of all or part of this set of data;
to allow the use of a method of successive approximations converging towards the fixed point of the said global contractive mapping;
all the said parameters thus determined and related to the m elementary sub-sets constituting a primary representation of the said set of data.
In this aspect of the present invention, the device for the primary processing of a set of data representing physical quantities includes:
means of inputting data to be processed;
means of outputting parameters,
first logic means of transforming the data to be processed into parameters; the said first logic means including:
xe2x80x9cpartitioning means adapted to partition the said set of data into xe2x80x9celementary sub-setsxe2x80x9d,
xe2x80x9cconstructionxe2x80x9d means adapted:
to take into account, for each of the said elementary sub-sets, n working sub-sets which correspond thereto, at least one of the said working sub-sets having a size different from that of the corresponding elementary sub-set, n being non-null,
to construct, for each of the elementary sub-sets, an elementary mapping belonging to the group of mappings consisting of multi-dimensional mappings and non-linear mappings, of the n working sub-sets in the elementary sub-set in question, determining all the parameters of this elementary mapping so as:
to make contractive a global mapping of the so-called xe2x80x9cfirst typexe2x80x9d including the m elementary mappings whose fixed point constitutes an approximation of all or part of this set of data;
to allow the use of a method of successive approximations converging towards the fixed point of the said global contractive mapping;
to deliver, at the output means, the parameters thus determined, said parameters constituting a primary representation of the said set of data.
These arrangements have substantially the same advantages as those relating to the first aspect of the present invention as described briefly above.
It should be noted in particular that, as the elementary mappings constructed belong to the group of mappings consisting of multi-dimensional mappings and non-linear mappings, the mappings belonging to the class of similitudes are avoided, with the advantages observed above.
In addition, the fact of providing that at least one working sub-set has a size different from that of the corresponding elementary sub-set makes it possible to broaden, for the expert, the choice of the type of elementary mapping which he will use, in order to constitute the global contractive mapping. In this way, the expert can even more easily adapt the implementation of the method to particular situations relating to data to be processed. In addition, by choosing working sub-sets having a size greater than that of the corresponding elementary sub-sets, the range of parameters corresponding to the elementary mappings is thereby broadened, which improves the quality of retrieval of data, and in particular when said data relate to an image.
In another of its aspects, the present invention relates to a method for the secondary processing of a set of data including a set of parameters resulting from the primary processing of initial data effected by implementing the methods described briefly above, characterised in that it includes:
c) an xe2x80x9citerative calculationxe2x80x9d step in the course of which, using the said set of parameters, use is made of a method of successive approximations converging towards the fixed point of a global contractive mapping of the so-called xe2x80x9csecond typexe2x80x9d, the latter fixed point constituting a secondary representation of the said set of initial data.
Moreover, in this aspect, the present invention relates to a device for the processing of data suitable for the secondary processing of a set of parameters resulting from the primary processing of the initial data produced by the use of one or other of the primary processing methods according to the first two aspects of the invention defined above, the data processing device being characterised in that it includes:
means of inputting parameters
means of outputting data;
second logic means of transforming the parameters into data; the said second logic means including:
xe2x80x9citerative calculationxe2x80x9d means adapted to implement, using the said set of parameters, a method of successive approximations converging towards the fixed point of a global contractive mapping of the so-called xe2x80x9csecond typexe2x80x9d, the latter fixed point constituting a secondary representation of the said set of initial data, and delivering the data thus calculated at the output means.
By virtue of these arrangements, it is possible to effect a secondary processing of a set of data having a set of parameters resulting from the primary processing of initial data in a relatively simple manner since it suffices to use a method of successive approximations, known per se, converging towards the fixed point of a global contractive mapping. The convergence process thus used makes it possible to approach a representation of the set of initial data. It is possible, advantageously, to fix an error threshold as from which it will be considered that the precision required for the representation of this set of initial data is achieved.
In this case, the implementation in the preferred embodiment, where the global contractive mapping used during the primary processing and the global contractive mapping used during the secondary processing are identical, the representation of the set of initial data reached at the end of the secondary processing in reality constitutes a retrieval of the said initial data with, where applicable, the predetermined error mentioned above. Thus, if the set of initial data relates to an image, the primary processing makes it possible to transform and/or to compress these data, for example with a view to their storage or transmission, and the secondary processing makes it possible to retrieve them.
In the case where the global contractive mapping implemented during the primary processing and the global contractive mapping implemented during the secondary processing are of distinct types, the secondary representation no longer constitutes a retrieval of the initial data but in reality constitutes a transformation thereof. This will be the case for example when an initial colour image has been the subject of a primary processing and is then represented by an image with one grey level: in both cases it is indeed the same image, however the data relating to the image obtained at the end of the secondary processing are no longer of the same type as the initial data.
In a preferred embodiment, in the course of the said xe2x80x9citerative calculationxe2x80x9d step, account is taken on the one hand of the said set of parameters and on the other hand of an arbitrary set of data referred to as the xe2x80x9cinitialisationxe2x80x9d set, and, in order to effect the said global contractive mapping of the so-called xe2x80x9csecond typexe2x80x9d:
c1) the initialisation set is partitioned into m elementary sub-sets;
c2) for each of the m elementary sub-sets thus determined, the parameters of the elementary mappings corresponding to the elementary sub-sets resulting from the partitioning of the set of initial data are taken into consideration, and the said elementary mappings are used on the elementary sub-sets of the initialisation set;
c3) the set of data obtained by the m implementations of elementary mappings are combined, this constituting an intermediate representation of the said initial data, with an error;
c4) operations c1-c3 are reiterated, taking the said intermediate representation as the initialisation set, so as to approach the fixed point of the said global contractive mapping of the second type;
the set of data finally obtained constituting a secondary representation of the set of data which was the subject of a primary processing.
In a preferred embodiment of the device according to the invention, the said second logic means include:
means of inputting parameters;
means of outputting data;
second logic means of transforming the parameters into data; the said second logic means including:
xe2x80x9citerative calculationxe2x80x9d means adapted to effect, using the said set of parameters, and on an arbitrary set of data referred to as an xe2x80x9cinitialisationxe2x80x9d set, a global contraction of the so-called xe2x80x9csecond typexe2x80x9d and, for this purpose:
c1) to partition the initialisation set into m elementary sub-sets,
c2) to take into consideration, for each of the m elementary sub-sets thus determined, the parameters of the elementary mappings corresponding to the elementary sub-sets resulting from the partitioning of the set of initial data, and to use the said elementary mappings on the elementary sub-sets of the initialisation set,
c3) to combine the set of data obtained by the m implementations of elementary mappings, this constituting an intermediate representation of the said initial data, with an error,
c4) to reiterate operations c1-c3, taking the said intermediate representation as the initialisation set, so as to approach the fixed point of the said global contractive mapping of the second type,
c5) to deliver, at the output means, the set of data thus obtained, this set constituting a secondary representation of the said set of initial data.
By virtue of these arrangements, the method of successive approximations used for the secondary processing is implemented in a particularly simple manner using the parameters obtained at the end of the primary processing.
The inventors noted, in the field of image processing with compression, the performance both with regard to the quality of the image retrieved and with regard to the speed of processing mentioned above.
The present invention also relates, in another of its aspects, to a method of processing a set of data representing a physical quantity comprising a primary processing phase and a secondary processing phase, the said processings being in accordance with those briefly defined above. Correlatively, the data processing device, according to this aspect of the invention, incorporates a primary processing device and a secondary processing device as defined above.
This aspect of the invention combines, within the same processing method, a primary processing phase and a secondary processing phase. These arrangements can be particularly advantageous should it be desired to transform data of one type into data of another type. Thus for example, in certain image processing applications, it may be useful to be able to transform a colour image into a grey-level image. According to this aspect of the invention, such a transformation will consist on the one hand of a primary processing of the colour image, followed (immediately or otherwise) by a secondary processing of the parameters thus obtained, in the course of which a global contractive mapping of the so-called xe2x80x9csecond typexe2x80x9d (different from the global contractive mapping effected during the primary processing) will be effected so as to retrieve a different type of image, in the example cited a grey-level image. This is an example of xe2x80x9ccomplex processingxe2x80x9d.